Averaging is a well-known approach to reduce the effect of noise on signal measurements. Averaging is a technique that can be used to reduce the impact of an unstable or random-like process that is present on an otherwise stable process. Averaging reveals the stable portion of the process by diminishing the contribution of the unstable process as the average progresses. For example, a frequency counter might average a number of measurements on a constant frequency signal to improve the resolution of the measurement.
Generally, to analyze the behavior of a signal over a period of time, a block of time-related measurements is taken. A display of amplitude measurements versus time will produce a waveform of the signal's behavior.
For repetitive signals, block averaging of the corresponding samples from successive measurement blocks will improve the resolution of the measurement. Amplitude block averaging methods are found on some digitizing sampling oscilloscopes (DSO).
The general approach to averaging signal amplitude versus time requires triggering each waveform block from a reference signal. If this reference provides an unambiguous voltage that identifies a time with respect to which the amplitude characteristics of the measured signal are repeating, then block averaging can be used to obtain improved amplitude resolution. This type of averaging is essentially one-dimensional: the y-axis values (voltage amplitude) of each update are averaged, but the x-axis values (time position) remain constant.
Additionally, continuous time interval measurements on a signal provide an approach to analyze characteristics of the signal in the modulation domain, i.e., the behavior of the frequency or phase of the signal versus time. This is different from classical ways of measuring and displaying data about signals. An oscilloscope shows amplitude versus time: the time domain. A spectrum analyzer shows amplitude versus frequency: the frequency domain. These continuous time interval measurements make it easier to study dynamic frequency behavior of a signal, for example, frequency drift over time of an oscillator, the frequency hopping performance of an agile transmitter, chirp linearity, and phase switching in radar systems.
An example of an instrument that makes continuous time interval measurements and generates data referred to as "time stamp" data is described in "Frequency and Time Interval Analyzer Measurement Hardware," Paul S. Stephenson, Hewlett-Packard Journal, Vol. 40, No. 1, February, 1989. Time stamp data comprises an event count and a time count for each measurement sample taken. The instrument disclosed by Stephenson includes measurement hardware that counts input signal cycle events and counts clock cycles from an internal clock, memory to store the measurement data, and a microprocessor for controlling the operation of the instrument and processing the measurement data.
The measurement data to be averaged comprises data taken by a measurement instrument, such as the frequency and time interval analyzer instrument described by Stephenson, above. Typically, the data is stored for processing after data acquisition has been completed. FIG. 1 shows a system block diagram of the instrument described by Stephenson. An input signal to be measured is applied to input amplifier 703 via input line 702. The input amplifier 703 preconditions the signal and converts it to binary form for input to the measurement hardware 701 via line 704. Measurement hardware 701 receives measurement setup and control instructions from the microprocessor 705 via line 706. Measurement hardware 701 acquires the measurement data from the input signal and stores the data in memory 707. The raw binary data acquired and stored by the measurement hardware 701 is provided to microprocessor 705 via line 706 for processing, either for display or for storage.
Now, block averaging is important for analyzing dynamic, repeating inputs, that are changing with time but eventually repeat in such a way that there is a stimulus to synchronize with repetition. VCO testing provides an example of this class of input. The applied voltage tuning step provides the synchronization that allows the measurement instrument to repetitively capture the frequency response.
However, the input may not be phase-coherent with respect to the synchronizing stimulus. Stated simply, phase coherence means that the measured input would be at the same phase every time the stimulus is applied. For the VCO example, if the VCO output were always at 90 degrees (maximum high voltage) when the tuning step was applied, it would be phase-coherent. Notice that phase coherence has nothing to do with the repeatability of the frequency at a given time. The VCO might have an arbitrary phase when the tuning step is applied, but it might also always be at 52.35 MHz at the time of the step. The lack of phase coherence introduces time variabilities in continuous time interval measurements that conventional block averaging methods have not been able to handle.